1. Field of the Invention
The present invention relates to techniques for resampling a quantized signal. More specifically, the present invention relates to a method and apparatus for resampling and quantizing a quantized signal using Barycentric Coordinate Techniques.
2. Related Art
As computer systems become more powerful, they are increasingly being used by businesses for mission-critical applications. For example, airlines are critically dependent on computer systems that manage flight reservations, and would essentially cease to function if these systems failed. Hence, monitoring the health of computer systems is very important because it allows a system administrator to detect problems and take preventive measures before a catastrophic failure occurs.
Telemetry signals are often used to monitor the health and the performance of a computer system. Telemetry signals typically represent physical variables such as temperature, voltage, current, vibration, acoustics, etc. Note that telemetry signals may also include software-based performance parameters, such as processor load, memory/cache usage, system throughput, queue lengths, I/O traffic, quality of service, security, etc.
Once these telemetry signals are received, they are typically fed into a fault-detection application that uses statistical analysis techniques and pattern recognition techniques to determine whether the computer system is experiencing hardware degradation. These fault detection applications typically require that the telemetry signals have uniform sampling intervals that represent a consistent snapshot of the system state at a particular instant in time.
However, since telemetry signals are collected from different collector processes, they are usually not synchronized. Note that, even if the collector processes sample the telemetry signals at the same rate and are started at the same time, they may actually produce unsynchronized signals because the acquisition rate of the collector process can speed up or slow down depending on the load on the computer system.
Unsynchronized telemetry signals can be synchronized by resampling them so that all sampled variables appear to have been sampled at exactly the same point in time. Resampling is typically performed by first interpolating a signal and then sampling the interpolated signal at new points in time. For example, a linear least squares fit can be used to resample the signal. However, if the linear least squares fit is applied to a signal in real time, the resampled signal can exhibit poor correlation to the original signal due to poor fitting in regions that contain dynamic variations. To better capture dynamic trends in the data, a cubic-spline fit, which preserves the first and second time derivatives of the signal, can be used. Unfortunately, the cubic-spline fit technique can create spurious values in the resampled signal when sampling rates are high. For these reasons, the statistical distribution of the resampled signal may turn out to be different from the original signal.
Unfortunately, statistical analysis techniques used in fault detection applications can be very sensitive to changes in the statistical distribution of the quantized values. Consequently, if telemetry signals are resampled naively, it can cause the statistical distribution of the resampled signals to be different from the original signals, which in turn, can cause the fault detection application to malfunction.
Hence, what is needed is a method and an apparatus for resampling a quantized signal that preserves the statistical distribution of the quantized values of the signal.